Question: Rewrite as a simplified fraction. ${0.3\overline{1} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 31.1111...\\ 10x &= 3.1111...\end{align*}}$ Subtracting the two equations, we have: ${90x = 28}$ ${x = \dfrac{28}{90}} $ ${x = \dfrac{14}{45}} $